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shminux comments on Other prespective on resolving the Prisoner's dilemma - Less Wrong
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Not sure how this is relevant to the OP, but clearly Omega would defect while making you cooperate, e.g. by convincing you that he is your PD-clone.
Superior (or even infinite) computing power does not imply he can make you be persuaded to cooperate, only that he knows whether you will. If there exist any words he could say to convince you to cooperate, he will say them and defect. However, if you cooperate only upon seeing omega cooperate (or prove that he will), he will cooperate.
The relevance is that the rational strategy is to defect. Always, unless your selection has a sufficiently high probability of changing your opponents suggestion. If possible, maximize the chances that your opponent will cooperate.
... unless your opponent also defects, and only in one-shot PD. Or maybe we are using different definitions of "rational", given how both players "rationally" defecting both lose.
Given that one's opponent defects, you get more points for defecting.